2,889 research outputs found
Mild Solutions for a Class of Fractional SPDEs and Their Sample Paths
In this article we introduce and analyze a notion of mild solution for a
class of non-autonomous parabolic stochastic partial differential equations
defined on a bounded open subset and driven by an
infinite-dimensional fractional noise. The noise is derived from an
-valued fractional Wiener process whose covariance operator
satisfies appropriate restrictions; moreover, the Hurst parameter is
subjected to constraints formulated in terms of and the H\"{o}lder exponent
of the derivative of the noise nonlinearity in the equations. We
prove the existence of such solution, establish its relation with the
variational solution introduced in \cite{nuavu} and also prove the H\"{o}lder
continuity of its sample paths when we consider it as an --valued
stochastic processes. When is an affine function, we also prove uniqueness.
The proofs are based on a relation between the notions of mild and variational
solution established in Sanz-Sol\'e and Vuillermot 2003, and adapted to our
problem, and on a fine analysis of the singularities of Green's function
associated with the class of parabolic problems we investigate. An immediate
consequence of our results is the indistinguishability of mild and variational
solutions in the case of uniqueness.Comment: 37 page
Alteración de las biotitas y biotitas clorizadas de la granodiorita de Collserola (Barcelona)
[ES] Se estudia la alteración natural experimentada por las biotitas y
biotitas cloritizadas de la granodiorita de la Serra de Collcerola (Barcelona),
bajo clima mediterráneo. Se muestrearon nueve perfiles, separándose
magnéticamente las biotitas de la fracción arena, analizándose
químicamente (elementos totales), por difractometría de R.X.
y microscopia electrónica de barrido. También se estudiaron con el
microscopio petrográfico láminas delgadas de muestras no
perturbadas.
Las biotitas evolucionan progresivamente primero a interestratificados
biotita-vermiculita y después a vermiculita, apreciándose una
tendencia a la esmectización, sugiriendo que las condiciones medioambitentales
en las que se ha producido la alteración son muy similares
a las actuales. La fase clorita procedente de las biotitas cloritizadas
permanece inalterada en dicho medio.[EN] The weathering of biotites and cloritized biotites from a granodiorite
from Serra de Collcerola (Barcelona, Spain), under mediterranean
climate, has been studied. The sand fraction from the horizons
of nine pedological profiles were sampled and the biotites magnetically
separated and analysed by XRD, SEM and chemically. Thin
sections of undisturbed samples were also studied.
The weathering sequence from non-cloritized biotites was Biotite - Interlayer B-V - Vermiculite with a trend towards smectitization.
The chlorite mineral from chloritized biotites remains unchanged
in this environment. These results suggest tliat the weathering
environment has been quite similar to the present one.Peer reviewe
Inclusion of chemical effect in a fully coupled THM finite element code
Bentonite-rich clays can be used as a buffer / backfill material in deep geological repositories for nuclear waste. The prediction of the long-term performance of a buffer / backfill in such a complex environment, where the temperature, humidity and chemistry of water change, requires a fully thermo-hydro-mechanical-chemical (THMC) coupled numerical code. This paper presents a simple extension of a THM coupled finite element code to include chemical effects. After deriving the governing salt mass balance equation and discussing its implementation into the code, the paper verifies the extended framework against an analytical solution for 1D salt transport. In addition, the article presents a validation example in which the code replicates experimental data. The numerical results obtained from the extended THMC coupled finite element code encourage further investigation of the chemical effects on the mechanical and thermal behaviour of the material, which would serve the ultimate goal of achieving a safer design of the nuclear waste storage facility.Postprint (published version
Analysis of strain localization with a nonlocal plasticity model
In the present paper a nonlocal plasticity model is described, intended to reproduce the mechanical behaviour of stiff fine-grained soils, including the objective simulation of strain localization; the phenomenon of accumulation of deformations in narrow zones in the form of shear bands or fractures. A number of analyses have been performed to assess the developed formulation. Relevant aspects have been addressed such as the thickness of the shear band, its orientation, and the onset of localization in a boundary value problem (BVP). Results provide useful insigths into relevant aspects of the numerical simulation of strain localization
A linear construction for certain Kerdock and Preparata codes
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes
are shown to be linear over \ZZ_4, the integers . The Kerdock and
Preparata codes are duals over \ZZ_4, and the Nordstrom-Robinson code is
self-dual. All these codes are just extended cyclic codes over \ZZ_4. This
provides a simple definition for these codes and explains why their Hamming
weight distributions are dual to each other. First- and second-order
Reed-Muller codes are also linear codes over \ZZ_4, but Hamming codes in
general are not, nor is the Golay code.Comment: 5 page
- …